Best Response in Competitive Markets

Hello! Welcome back to your course on game theory for entrepreneurs.

In our last lesson, we focused on predicting a competitor's likely reaction to your market entry. We saw how thinking from their perspective and considering their payoffs could help you determine if their threats (like starting a price war) were credible. We used a game tree to visualize this in a sequential "entry game."

Today, we'll sharpen that predictive skill by formalizing it into a core concept of game theory: best response. This lesson will equip you with a systematic way to determine your optimal move in any competitive situation, which is the final piece of our foundational module. By the end of this lesson, you will be able to apply 'best response' thinking to a simple competitive scenario in your own market.

What is Your Best Move? Defining "Best Response"

The idea of "best response" is simple but powerful: Given what you believe your competitor will do, what is the single best action you can take?

In the last lesson, we did this intuitively when analyzing the game tree. We asked, "If you enter, what is the incumbent's best move?" and saw they would choose to "accommodate" because it gave them a higher payoff than "fight."

To make this thinking more rigorous, especially when players might be moving at the same time, we need a formal definition and a structured way to analyze the situation.

The following reading from a textbook by researchers at Cornell University provides a clear, step-by-step introduction to "best response" and a related idea, "dominant strategy."

The key takeaway is that you analyze a game by breaking it down. You put yourself in your competitor's shoes, consider one of their potential moves, and ask, "If they do that, what's my best response?" Then you repeat this for all their other possible moves.

The Ultimate Move: The Dominant Strategy

The reading introduced a crucial concept: the strictly dominant strategy. This is a strategy that is your best response no matter what your competitor does.

Finding a dominant strategy is like finding a golden key.

• If you have one, your decision becomes simple: you should play it.
• If you can see that your competitor has one, their move becomes predictable: you can be confident they will play it.

This allows you to simplify a complex, uncertain situation. Let's see this in a business context using another part of the same reading.

This two-step logic is fundamental:

1. Look for any dominant strategies.
2. Use that knowledge to predict behavior and determine your own best response.

Here is a visual representation of a payoff matrix where one player, Samsung, has a dominant strategy.

Applying Best Response to Your Woodworking Business

Let's apply this to a critical decision for your new venture: pricing.

Imagine you're deciding between two initial strategies:

• Premium Price: Target the high end, emphasizing the quality and precision from your CNC machinery.
• Competitive Price: Price your products similarly to existing local makers to attract initial customers.

Your main competitor, "Traditional Cabinets Inc.", also has choices. Let's say they can either Maintain their Price or Cut their Price to try and push you out.

Let's map this out in a payoff matrix. The numbers represent your potential monthly profit (first number, in blue) and your competitor's profit (second number, in green), in thousands of dollars.

	Competitor: Maintain Price	Competitor: Cut Price
You: Premium Price	10, 8	4, 6
You: Comp. Price	7, 5	2, 3

Now, let's find the best responses for each player.

Your Best Response:

1. Assume your competitor chooses to Maintain Price. Your choices are Premium Price (payoff of 10) or Competitive Price (payoff of 7). Your best response is Premium Price.
2. Assume your competitor chooses to Cut Price. Your choices are Premium Price (payoff of 4) or Competitive Price (payoff of 2). Your best response is again Premium Price.

Since "Premium Price" is your best response no matter what they do, it is your dominant strategy.

Competitor's Best Response:

1. Assume you choose Premium Price. Their choices are Maintain Price (payoff of 8) or Cut Price (payoff of 6). Their best response is to Maintain Price.
2. Assume you choose Competitive Price. Their choices are Maintain Price (payoff of 5) or Cut Price (payoff of 3). Their best response is again to Maintain Price.

Your competitor also has a dominant strategy: "Maintain Price".

Because both of you have dominant strategies, we can predict the outcome with high confidence: you will set a premium price, and your competitor will maintain their current pricing, leading to profits of ($10k for you, $8k for them).

Test your understanding!

Let's change one number. Suppose an aggressive price cut from your competitor is much more damaging to you. If you set a Premium Price and they Cut Price, your payoff is now -2 (a loss) instead of 4.

	Competitor: Maintain Price	Competitor: Cut Price
You: Premium Price	10, 8	-2, 6
You: Comp. Price	7, 5	2, 3

Does "Premium Price" remain your dominant strategy? What is your best response now if they cut their price?

Show answer

No, "Premium Price" is no longer your dominant strategy.

• If they Maintain Price, your best response is still Premium Price (10 > 7).
• But if they Cut Price, your best response is now Competitive Price (-2 < 2).

Since your best response changes depending on what they do, you no longer have a dominant strategy. Your decision is more complex and depends heavily on how likely you think they are to cut their price.

This type of interdependent pricing decision, where both firms might be tempted to cut prices, is very common. Let's watch a video that illustrates this with a famous business rivalry.

Conclusion

You have now completed the first module of the course and have a solid set of foundational tools for strategic thinking. Today's lesson on "best response" is the engine that drives game theory analysis. By methodically analyzing the game from each player's perspective, you can move from simple guesswork to structured prediction.

Key Takeaways:

• Best Response: Your optimal action, assuming a specific action from your competitor.
• Systematic Analysis: You can find best responses by analyzing a payoff matrix, considering each of your competitor's potential moves in turn.
• Dominant Strategy: A strategy that is your best response to all of your competitor's moves. This is a powerful tool for simplifying decisions and predicting outcomes.
• Predicting Outcomes: By finding the best responses for all players, you can often predict the most likely result of a competitive interaction.

Preview of the Next Lesson:

In the next module, we will begin organizing these concepts into the core models of game theory. We have already seen two different kinds of interactions: the sequential market entry game from the last lesson and the simultaneous pricing game from this one. In our next lesson, we will formally distinguish between simultaneous-move and sequential-move games, which is the first step in learning to select the right analytical tool for the specific business challenge you face.